Write 78/115 as a decimal fraction
0.678260870...
To write 78/115 as a decimal fraction, you can divide 78 by 115 using long division or a calculator. The result is approximately 0.6782608695652174.
To write 78/115 as a decimal fraction, you need to divide the numerator (78) by the denominator (115). Here's how you can do it:
1. Set up the long division problem with 78 as the dividend and 115 as the divisor:
```
0._____
115)78
```
2. Start dividing: How many times does 115 go into 78? The answer is 0, so you write "0" above the division line and carry the remainder (78) down next to the 8:
```
0._____
115)78
0
```
3. Add a decimal point after the zero you wrote, indicating the start of the fractional part:
```
0.
115)78
0
```
4. Since we have a remainder of 78, we need to extend the decimal fraction by adding zeros after the decimal point:
```
0._____
115)7800
0
```
5. Now, divide 115 into 7800. How many times does 115 go into 7800? The answer is 67, so you write "67" above the division line and subtract (67 * 115) from 7800. The result is 55:
```
0.67_____
115)7800
690
-----
900
...
```
6. Bring down the next digit (a zero) from the dividend and append it to the previous result (55):
```
0.67_____
115)7800
690
-----
900
805
----
...
```
7. Repeat the process, dividing 115 into 805. This time, the answer is 7, so you write "7" above the division line and subtract (7 * 115) from 805. The result is 70:
```
0.678_____
115)7800
690
-----
900
805
----
95
...
```
8. Continue bringing down zeros as needed, and repeat the division until you achieve the desired level of accuracy or if the pattern repeats. Here, you can see that 115 keeps dividing evenly into 950, resulting in a repeating pattern of 0.678, which can be denoted as 0.678(n), where n represents the repeating digit or group.
Therefore, 78/115, when written as a decimal fraction, is approximately 0.678.